(a-1)-2a%2B2.jpeg "(a+1)(a-1)-2a+2")
Factoring and Simplifying (a+1)(a-1)-2a+2
This expression can be simplified and factored using algebraic techniques. Here's how:
1. Expanding the Expression
First, we expand the expression using the difference of squares pattern: (a+1)(a-1) = a² - 1.
Our expression now becomes: a² - 1 - 2a + 2
2. Combining Like Terms
Next, we combine the constant terms: -1 + 2 = 1
The simplified expression is: a² - 2a + 1
3. Factoring the Quadratic
The expression is now in the form of a quadratic equation, which can be factored. We look for two numbers that add up to -2 (the coefficient of the middle term) and multiply to 1 (the constant term). These numbers are -1 and -1.
Therefore, the factored form of the expression is: (a - 1)(a - 1) or (a - 1)²
Conclusion
The fully simplified and factored form of the expression (a+1)(a-1)-2a+2 is (a - 1)².